Write the equation of a line whose slope is the same as the line y=-2x=7 and whose y-intercept is the same as the line 2y=x-8.

2y = x - 8

Replace x with 0 and solve for y:
2y = 0 - 8
Y = -4 = y-int.

Eq: Y = -2x - 4

To find the equation of a line with a given slope and y-intercept, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.

Given that the slope of the line is the same as y = -2x + 7, we know that m = -2.

Similarly, the y-intercept of the line is the same as 2y = x - 8. To find the y-intercept, we need to isolate y on one side of the equation. Dividing both sides of 2y = x - 8 by 2, we get y = (1/2)x - 4.

Therefore, the y-intercept, b, is -4.

Now we have enough information to write the equation of the line:

y = mx + b

Substituting the values we found, the equation becomes:

y = -2x - 4.

To find the equation of a line with a specific slope and y-intercept, we can use the slope-intercept form of a linear equation, which is given by "y = mx + b," where "m" represents the slope and "b" represents the y-intercept.

First, let's find the slope of the line y = -2x + 7. In this equation, the coefficient of "x" is -2, which represents the slope. Hence, the slope of this line is -2.

Next, let's find the y-intercept of the line 2y = x - 8. To convert this equation into slope-intercept form, we need to isolate the y-variable. Dividing the equation by 2, we get y = (1/2)x - 4. Comparing this equation with the slope-intercept form, we can see that the y-intercept is -4.

Therefore, we have the slope (-2) and the y-intercept (-4) needed to write the equation of the line. Plugging these values into the slope-intercept form, we get:

y = -2x - 4

Thus, the equation of the line with the same slope as y = -2x + 7 and the same y-intercept as 2y = x - 8 is y = -2x - 4.